Speaker identification is an important topic with relevance to various disciplines. This paper proposes a novel speaker identification system, which consists of two major components-feature extraction and sparse representation classifier (SRC). Although SRC has been utilized for many classification purposes, few studies have provided insight into the link between the commonly used speaker identification feature, i-vector, and SRC. To combine i-vector and SRC sufficiently, we use probabilistic principal component analysis and Bartlett test to extract high-quality i-vector to construct a discriminative dictionary in SRC, supporting effective speaker identification. Besides improving dictionary from the i-vector aspect, we also utilize dictionary learning to further enhance the content of the dictionary. Two learning methods are proposed-robust principal component analysis dictionary and SVD-dictionary. Furthermore, we propose constructing a noise dictionary and combine it with the original dictionary to absorb and suppress noise when implementing the sparse coding. Various coding methods are utilized and analyzed. A comparison to the methods for speaker identification reveals that the proposed method outperforms the baselines and confirms its feasibility.